Articles publicats en revistes (Matemàtiques i Informàtica)

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Interval hypergraphic lattices
(Elsevier Ltd., 2026-02-01) Bergeron, Nantel; Pilaud, Vincent
For a hypergraph ℍ on [ ] , the hypergraphic poset ℍ is the transitive closure of the oriented skeleton of the hypergraphic polytope △ℍ (the Minkowski sum of the standard simplices △ for all ∈ℍ ). Hypergraphic posets include the weak order for the permutahedron (when ℍ is the complete graph on [ ] ) and the Tamari lattice for the associahedron (when ℍ is the set of all intervals of [ ] ), which motivates the study of lattice properties of hypergraphic posets. In this paper, we focus on interval hypergraphs, where all hyperedges are intervals of [ ] . We characterize the interval hypergraphs for which is a lattice, a distributive lattice, a semidistributive lattice, and a lattice quotient of the weak order.
Lp estimates for the Laplacian via blow-up
(Elsevier, 2025-10-05) Lewenstein Sanpera, Jan Bruno; Ros, Xavier
In this note we provide a new proof of the 2, Calderón-Zygmund regularity estimates for the Laplacian, i.e., Δ⁢ = and its parabolic counterpart ∂ − Δ⁢ = . Our proof is an adaptation of a contradiction and compactness argument that so far had been only used to prove estimates in Hölder spaces. This new approach is simpler than previous ones, and avoids the use of any interpolation theorem.
Bridging the Quality Gap: Robust Colon Wall Segmentation in Noisy Transabdominal Ultrasound
(Elsevier Ltd., 2025-10-01) Gago, Lucas; Fernández González, Miguel Á.; Engelmann, Justin; Remeseiro López, Beatriz; Igual Muñoz, Laura
Colon wall segmentation in transabdominal ultrasound is challenging due to variations in image quality, speckle noise, and ambiguous boundaries. Existing methods struggle with low-quality images due to their inability to adapt to varying noise levels, poor boundary definition, and reduced contrast in ultrasound imaging, resulting in inconsistent segmentation performance. We present a novel quality-aware segmentation framework that simultaneously predicts image quality and adapts the segmentation process accordingly. Our approach uses a U-Net architecture with a ConvNeXt encoder backbone, enhanced with a parallel quality prediction branch that serves as a regularization mechanism. Our model learns robust features by explicitly modeling image quality during training. We evaluate our method on the C-TRUS dataset and demonstrate superior performance compared to state-of-the-art approaches, particularly on challenging low-quality images. Our method achieves Dice scores of 0.7780, 0.7025, and 0.5970 for high, medium, and low-quality images, respectively. The proposed quality-aware segmentation framework represents a significant step toward clinically viable automated colon wall segmentation systems.
On the convergence of flow map parameterization methods for whiskered tori in quasi-periodic Hamiltonian systems
(Elsevier B.V., 2024-01-12) Fernández Viciana, Ana; Haro, Àlex; Mondelo Martell, Manel
We obtain an a-posteriori theorem for the existence of partially hyperbolic invariant tori in analytic Hamiltonian systems: autonomous, periodic, and quasi-periodic. The method of proof is based on the convergence of a KAM iterative scheme to solve the invariance equations of tori and their invariant bundles under the framework of the parameterization method. Starting from parameterizations analytic in a complex strip and satisfying their invariance equations approximately, we derive conditions for the existence of analytic parameterizations in a smaller strip satisfying the invariance equations exactly. The proof relies on the careful treatment of the analyticity loss with each iterative step and on the control of geometric properties of symplectic flavour. We also provide all the necessary explicit constants to perform computer-assisted proofs.
Explicit numerical computation of normal forms for Poincaré maps
(Elsevier B.V., 2025-05-10) Gimeno i Alquézar, Joan; Jorba i Monte, Àngel; Jorba Cuscó, Marc; Zou, Maorong
We present a methodology for computing normal forms in discrete systems, such as those described by Poincaré maps. Our approach begins by calculating high-order derivatives of the flow with respect to initial conditions and parameters, obtained via jet transport, and then applying appropriate projections to the Poincaré section to derive the power expansion of the map. In the second step, we perform coordinate transformations to simplify the local power expansion around a dynamical object, retaining only the resonant terms. The resulting normal form provides a local description of the dynamics around the object, and shows its dependence on parameters. Notably, this method does not assume any specific structure of the system besides sufficient regularity. To illustrate its effectiveness, we first examine the well-known Hénon–Heiles system. By fixing an energy level and using a spatial Poincaré section, the system is represented by a 2D Poincaré map. Focusing on an elliptic fixed point of this map, we compute a high-order normal form, which is a twist map obtained explicitly. This means that we have computed the invariant tori inside the energy level of the Poincaré section. Furthermore, we explore how both the fixed point and the normal form depend on the energy level of the Poincaré section, deriving the coefficients of the twist map as a power series of the energy level. This approach also enables us to obtain invariant tori inside nearby energy levels. We also discuss how to obtain the frequencies of the torus for the flow. We include a second example involving an elliptic periodic orbit of the spatial Restricted Three-Body Problem. In this case the map is 4D, and the normal form is a multidimensional twist map.
Periodic perturbation of a 3D conservative flow with a heteroclinic connection to saddle-foci
(Elsevier B.V., 2025-04-01) Murillo López, Ainoa; Vieiro Yanes, Arturo
The 2-jet normal form of the elliptic volume-preserving Hopf-zero bifurcation provides a one-parameter family of volume-preserving vector fields with a pair of saddle-foci points whose 2-dimensional invariant manifolds form a 2-sphere of spiralling heteroclinic orbits. We study the effect of an external periodic forcing on the splitting of these 2-dimensional invariant manifolds. The internal frequency (related to the foci and already presented in the unperturbed system) interacts with an external one (coming from the periodic forcing). If both frequencies are incommensurable, this interaction leads to quasi-periodicity in the splitting behaviour, which is exponentially small in (a suitable function of) the unfolding parameter of the Hopf-zero bifurcation. The corresponding behaviour is described by a Melnikov function. The changes of dominant harmonics correspond to primary quadratic tangencies between the invariant manifolds. Combining analytical and numerical results, we provide a detailed description of the asymptotic behaviour of the splitting under concrete arithmetic properties of the frequencies.
Safeguarding Autonomy: a Focus on Machine Learning Decision Systems
(Elsevier B.V., 2025-10-10) Subías Beltrán, Paula; Pujol Vila, Oriol; Lecuona Ramírez, Itziar de
As global discourse on AI regulation gains momentum, this paper focuses on delineating the impact of ML on autonomy and fostering awareness. Respect for autonomy is a basic principle in bioethics that establishes people as decision-makers. While the concept of autonomy in the context of ML appears in several European normative publications, it remains a theoretical concept that has yet to be widely accepted in ML practice. Our contribution is to bridge the gap between theory and practice in ML by encouraging the respect of autonomy in ML-aided decision-making. We do this by proposing a clear framework for operationalizing autonomy and identifying the conditioning factors that currently prevent it. Consequently, we focus on the different stages of the ML pipeline to identify the potential effects on ML end-users’ autonomy. To improve its practical utility, we propose a related question for each detected impact, offering guidance for identifying possible focus points to respect ML end-users autonomy in decision-making.
Formal stationary phase for the Mellin transform of a $\mathcal{D}$-module
(Research Institute for Mathematical Sciences, 2023-10-11) García López, Ricardo, 1962-
Given a holonomic $\mathbb{C}\left[z, z^{-1}\right]\left\langle\partial_z\right\rangle$-module $\mathbb{M}$, following Loeser and Sabbah (Comment. Math. Helv. 66 (1991), 458503), one can consider its Mellin transform, which is a difference system on the affine line over $\mathbb{C}$. In this note we prove a stationary phase formula, which shows that its formal behavior at infinity is determined by the local germs defined by $\mathbb{M}$ at its singular points.
Unit-Centric Regularization for Efficient Deep Neural Networks
(Institute of Electrical and Electronics Engineers (IEEE), 2025-07-21) Riera Molina, Carles Roger; Puertas i Prats, Eloi; Pujol Vila, Oriol
Deep neural networks excel by learning hierarchical representations, often requiring architectural enhancements like increased width, normalization layers, or skip connections, each adding complexity and computational cost. This paper proposes Jumpstart, a novel regularization technique that enables the use of simpler architectures by promoting efficient utilization of both network units and data points. The method penalizes units that become inactive (dead) or operate strictly in the linear regime, as well as data points whose activations within a layer are uniformly zero or strictly positive. This strategy enables the training of plain ReLU networks without relying on overparameterization, specialized initialization, normalization layers, or architectural modifications like skip connections. As a result, it promotes more efficient use of units and data, maintaining performance while avoiding waste of computational resources during both training and inference. On the ImageNet benchmark, it matches the top-1 accuracy of a standard ResNet50 with Batch Normalization and skip connections. On UCI tabular datasets, it consistently outperforms batch normalization and often surpasses residual connections. The method is evaluated using four global metrics: Dead Units, Linear Units, Trainability, and Convergence. Jumpstart significantly reduces the presence of inactive and linear units (0.07 and 0.12, respectively), outperforming most baselines and achieves superior trainability (1.0) and convergence (-0.03). These results demonstrate that simpler, regularized networks can maintain competitive accuracy while significantly lowering architectural complexity and computational burden. Jumpstart offers a sustainable and effective alternative to conventional deep learning design strategies, facilitating efficient training without compromising performance.
Hodge–Lyubeznik numbers
(Elsevier Masson, 2025-03-25) García López, Ricardo, 1962-; Sabbah, Claude
We define a Hodge-theoretical refinement of the Lyubeznik numbers for local rings of complex algebraic varieties. We prove that these numbers are independent of the choices made in their definition and that, for the local ring of an isolated singularity, they can be expressed in terms of the Hodge numbers of the cohomology of the link of the singularity. We give examples of isolated singularities with the same Lyubeznik numbers but different Hodge–Lyubeznik numbers.
Bridging gaps in youth mental health care: YOUTHreach—a comprehensive European strategy
(Springer Verlag, 2026-04-25) Oidermaa, Anna-Kaisa; Bechdolf, Andreas; Evers, Silvia; van Mastrigt, Ghislaine; Horstkötter, Dorothee; Janssen, Ricky; Bulgheroni, Maria; McDaid, David; Boehnke, Jan R.; McGorry, Patrick; van Amelsvoort, Therese; Boonstra, Anouk; Lekadir, Karim, 1977-; Ruiz Pujadas, Esmeralda; Broome, Matthew R.; Griffiths, Sian Lowri; Donohoe, Gary; Popma, Arne; Girolamo, Giovanni de; Díaz Caneja, Covadonga M.; Álvarez Jiménez, Mario; AEGEE; Schick, Anita; Reininghaus, Ulrich; Leijdesdorff, Sophie
Europe is facing a mental health crisis that will last for decades, impacting the long-term health outcomes, wellbeing and economic productivity of our current generation of young people. Yet, large-scale, comparative research of youth-friendly mental health interventions is lacking. The YOUTHreach consortium aims to bridge this gap and provide a comprehensive European strategy. For this purpose, YOUTHreach will evaluate the clinical effectiveness and cost-effectiveness of three existing and accessible innovative interventions for prevention and early intervention of mental ill-health in youth, developed and tested in co-creation with youth: 1) YEAH, walk-in youth mental health support centres; 2) SELFIE, a transdiagnostic blended ecological momentary intervention; and 3) MOST, a clinical and peer-moderated digital youth mental health platform. In addition, feasibility and acceptability at new sites across Europe will be tested. Furthermore, in partnership with young people, best practice recommendations will be developed based on existing and new data and built into an integrated European youth mental health framework. Finally, awareness and accessibility of these interventions among policymakers, healthcare professionals, the general public, and youth—the target group—will be raised. YOUTHreach aims to contribute towards transformation of the present traditional mental healthcare system and providing the next generation with a better perspective in terms of health, wellbeing and productivity.
The canonical module of GT-varieties and the normal bundle of RL-varieties.
(Springer Verlag, 2021) Colarte Gómez, Liena; Miró-Roig, Rosa M. (Rosa Maria)
In this paper, we study the geometry of GT-varieties with group a finite cyclic group of order d. We prove that the homogeneous ideal of is generated by binomials of degree at most 3 and we provide examples reaching this bound. We give a combinatorial description of the canonical module of the homogeneous coordinate ring of and we show that it is generated by monomial invariants of of degree d and 2d. This allows us to characterize the Castelnuovo–Mumford regularity of the homogeneous coordinate ring of . Finally, we compute the cohomology table of the normal bundle of the so-called RL-varieties. They are projections of the Veronese variety which naturally arise from level GT-varieties.
Lacunary polynomials in L1: Geometry of the unit sphere
(Elsevier B.V., 2021-04-16) Dyakonov, Konstantin M.
Let Λ be a finite set of nonnegative integers, and let be the linear hull of the monomials with , viewed as a subspace of on the unit circle. We characterize the extreme and exposed points of the unit ball in .
A counterexample to Payne's nodal line conjecture with few holes
(Elsevier B.V., 2021) Dahne, Joel; Gómez Serrano, Javier; Hou, Kimberly
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with many holes and raised the question of the minimum number of holes a counterexample can have. In this paper we prove it is at most 6.
Gaussian lower bound and positivity of the density of stochastic delay differential equations driven by a fractional Brownian motion
(Sveuilište Josipa Jurja Strossmayera u Osijeku, 2026-04-02) Burés Mogollón, Òscar; Rovira Escofet, Carles
In this paper, we prove that the density of a stochastic delay differential equation driven by a fBm with Hurst parameter > 1/2 is strictly positive combining Nourdin-Viens’ and Kohatsu-Higa’s method.
Closure properties of measurable ultrapowers
(Association for Symbolic Logic., 2021-05-06) Lücke, Philipp; Müller, Sandra
We study closure properties of measurable ultrapowers with respect to Hamkin’s notion of freshness and show that the extent of these properties highly depends on the combinatorial properties of the underlying model of set theory. In one direction, a result of Sakai shows that, by collapsing a strongly compact cardinal to become the double successor of a measurable cardinal, it is possible to obtain a model of set theory in which such ultrapowers possess the strongest possible closure properties. In the other direction, we use various square principles to show that measurable ultrapowers of canonical inner models only possess the minimal amount of closure properties. In addition, the techniques developed in the proofs of these results also allow us to derive statements about the consistency strength of the existence of measurable ultrapowers with non-minimal closure properties.
The basepoint-freeness threshold of a very general abelian surface
(Springer Nature, 2022-01-07) Rojas González, Andrés
For abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepoint-freeness threshold. Our main tool is the relation between cohomological rank functions and Bridgeland stability. In virtue of recent results of Caucci and Ito, these computations provide new information on the syzygies of polarized abelian surfaces.
Convex analysis on polyhedral spaces
(Springer Verlag, 2022-01-24) Botero, Ana María; Burgos Gil, José I.; Sombra, Martín
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
Steel’s Programme: Evidential Framework, the Core and Ultimate-L
(Association for Symbolic Logic., 2023) Bagaria, Joan; Ternullo, Claudio
We address Steel’s Programme to identify a ‘preferred’ universe of set theory and the best axioms extending ZFC by using his multiverse axioms MV and the ‘core hypothesis’. In the first part, we examine the evidential framework for MV, in particular the use of large cardinals and of ‘worlds’ obtained through forcing to ‘represent’ alternative extensions of ZFC. In the second part, we address the existence and the possible features of the core of MVT (where T is ZFC+Large Cardinals). In the last part, we discuss the hypothesis that the core is Ultimate-L, and examine whether and how, based on this fact, the Core Universist can justify V=Ultimate-L as the best (and ultimate) extension of ZFC. To this end, we take into account several strategies, and assess their prospects in the light of MV’s evidential framework.
Invariant manifolds near L1 and L2 in the Sun–Jupiter elliptic restricted three-body problem I
(Springer Verlag, 2024-08-01) Duarte, Gladston; Jorba i Monte, Àngel
In this paper, we present a way of combining the computation of invariant tori and their stable and unstable manifolds with the multiple shooting technique. We start by showing some of the results of Jorba (Nonlinearity 14(5):943–976, 2001) that should be modified in order to introduce the multiple shooting technique in these computations. After that, by a direct application in the planar elliptic restricted three-body problem (PERTBP), how to modify the equations and methods to compute the above-mentioned objects is introduced. In particular, the structure of the (systems of) equations and matrices involved in these computations is shown. An application of these computations can be found in Duarte and Jorba (Invariant manifolds of tori near and in the planar elliptic restricted three-body problem II. The Dynamics of Comet Oterma, Preprint 2023), where the dynamics of comet 39P/Oterma is modelled as a PERTBP.

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